EXCHANGE 


™' 


J9PUlo 


Uniformity  in  Invcrtasc  Action 


By 
DAVID  INGERSOLL  HITCHCOCK 


DISSERTATION 

SUBMITTED  IN  PARTIAL  FULFILMENT  OF  Tim  REQUIREMENTS  FOR  Tim 

DEGREE  OF  DOCTOR  OF  PHILOSOPHY  IN  THE  FACULTY 

OF  PURE  SCIENCE,  COLUMBIA  UNIVERSITY 


Jfotu  1  ark  <Efti} 

1922 


Uniformity  in  Invertase  Action 


By 
DAVID  INGERSOLL  HITCHCOCK 


DISSERTATION 

SUBMITTED  IN  PARTIAL  FULFILLMENT  OF  THE  REQUIREMENTS  FOR  THE 

DEGREE  OF  DOCTOR  OF  PHILOSOPHY  IN  THE  FACULTY 

OF  PURE  SCIENCE,  COLUMBIA  UNIVERSITY 


fork  ffitty 

1922 


TO  MY  FATHER  AND  MOTHER 


478726 


ACKNOWLEDGMENT 

The  author  desires  to  express  his  sincere  gratitude  to  Professor  John 
M.  Nelson  for  his  kindly  direction  of  this  work.  He  wishes  also  to  thank 
Dr.  Warren  C.  Vosburgh  for  much  friendly  advice. 

To  the  Harriman  Research  Laboratory,  New  York  City,  thanks  are  due 
for  financial  assistance  which  made  this  work  possible. 

D.  I.  H. 

LABORATORY  OP  ORGANIC  CHEMISTRY, 

COLUMBIA  UNIVERSITY 

AUGUST,  1921 


ABSTRACT  OF  DISSERTATION. 

1 .  What  was  attempted  ? 

2.  How  far  were  the  attempts  successful? 

3.  What  contribution  actually  new  to  the  science  of  Chemistry  has 
been  made? 

1.  (a)  An  attempt  was  made  to  determine  whether  or  not  different 
preparations  of  the  enzyme  invertase  would  cause  the  hydrolysis  of  cane 
to  proceed  at  correspondingly  identical  rates  in  parallel  experiments. 

(b)  A  further  attempt  was  made  to  find  a  general  expression  for 
the  normal  course  of  the  hydrolysis  of  sucrose  by  invertase  under  varied 
conditions    of   enzyme    concentration,    temperature,    and   hydrogen-  ion 
concentration. 

(c)  Attempts  were  also  made  to  determine  whether  the  action  of 
different  invertase  preparations  could  be  modified  so  as  to  make  them  all 
act  alike. 

2.  (a)  It  was  found  that  not  all  invertase  preparations  act  quantita- 
tively alike  throughout  the  hydrolysis,  a  few  preparations  allowing  the 
reaction  to  become  abnormally  slow  after  the  first  twenty  per  cent  of  the 
inversion.  . 

(6)  For  the  normal  invertase  preparations  it  was  found  that  the 
hydrolysis-time  curves  coincided  exactly  if  the  proper  amounts  of  inver- 
tase were  used.  An  empirical  equation  was  obtained  and  so  transformed 
as  to  become  generally  applicable  to  hydrolyses  in  which  different  amounts 
of  invertase  were  used.  It  was  shown  that  within  certain  limits  this  equa- 
tion represented  the  course  of  the  hydrolysis  not  only  for  experiments  in 
which  the  invertase  concentration  was  varied,  but  also  for  experiments 
in  which  the  temperature  and  hydrogen  ion  concentration  were  varied. 
It  was  also  shown  that  this  equation  could  be  used  as  a  criterion  of  normal 
invertase  action. 

(c)  It  was  found  that  the  abnormal  course  of  the  reaction  due  to 
one  invertase  preparation  could  be  obviated  by  the  addition  of  boiled 
normal  in\ertase  or  of  sodium  chloride,  while  the  action  of  another  ab- 
normal invertase  preparation  was  not  affected  by  these  additions.  It 
was  found  that  a  normal  invertase  preparation  could  not  be  rendered 
abnormal  by  further  dialysis  or  by  partial  inactivation  by  heat  or  by 
ultraviolet  light. 

3.  The  new  contributions  made  in  the  present  work  are  as  follows: 

(a)  Not  all  invertase  preparations  act  identically  in  hydrolyzing 
sucrose,  a  few  being  abnormal  in  allowing  the  reaction  to  slow  up  after 
the  first  twenty  per  cent  more  than  is  the  case  with  the  normal  majority 
of  invertase  preparations. 

(b)  For  the  hydrolysis  of  sucrose  by  normal  invertase  preparations, 
the  time  of  reaction  has  for  the  first  time  been  exactly  expressed  as  a  de- 
finite function  of  the  per  cent  hydrolyzed.     It  has  been  shown  that  this 
function  is  of  the  same  form  for  changes,  within  certain  limits,  in  the 
invertase  concentration,  temperature,  and  hydrogen  ion  concentration. 
The  equation  expressing  this  function  yields  a  constant  which  is  the  most 
satisfactory  measure  so  far  proposed  of  the  true  activity  of  the  invertase. 

(c)  It  has  been  found  that  the  abnormality  of  one  abnormal  inver- 
tase preparation  is  removed  by  the  presence  of  boiled  normal  invertase  or 
sodium  chloride,  while  that  of  another  is  not,  and  also  that  the  normal 
invertase  cannot  be  made  abnormal  either  by  dialysis  or  by  the  action  of 
heat  or  of  ultraviolet  light. 


UNIFORMITY  IN  INVERTASE  ACTION. 

I.    Introduction. 

The  study  of  the  nature  of  enzymes  has  developed  chiefly  along  two 
distinct  lines.  So  far  all  attempts  to  isolate  an  enzyme  as  a  pure  substance 
of  definite  chemical  composition  have  been  without  satisfactory  results. 
Accordingly  considerable  work  has  been  done  to  gain  an  insight  into  the 
nature  of  the  enzyme  itself  by  studying  the  velocity  of  the  reaction  which 
is  catalyzed  by  the  enzyme.  The  object  in  all  these  researches  on  the 
chemical  kinetics  of  enzyme  action  has  been  to  find  some  general  law  gov- 
erning the  rate  of  the  reaction,  and  by  means  of  this  to  make  deductions 
concerning  the  mechanism  of  the  action  and  the  nature  of  the  enzyme. 

In  all  such  work  the  tacit  assumption  has  been  made  that  any  two 
preparations  of  the  same  enzyme,  if  the  same  amount  of  active  enzyme 
is  present,  and  other  conditions  are  the  same,  will  catalyze  the  reaction 
at  identical  rates  at  corresponding  points  throughout.  In  other  words, 
if  the  course  of  the  reaction  were  plotted,  the  .two  curves  should  be  super- 
imposable.  While  this  assumption  has  not  been  definitely  stated  in  the 
past,  it  is  a  necessary  implication  of  the  attempt  to  find  a  general  law  for 
the  rate  of  the  catalyzed  reaction.  Accordingly  it  seemed  desirable, 
before  going  further  in  the  attempt  to  obtain  a  general  law  for  the  hydrol- 
ysis of  cane  sugar  by  the  catalytic  action  of  invertase,  to  find  out  by  direct 
experiment  whether  several  different  enzyme  preparations  would  really 
give  the  same  quantitative  course  to  the  reaction. 

II.    Differences  in  Invertase  Action. 

In  order  to  make  this  comparison,  it  was  necessary  to  have  all  the  con- 
ditions alike  except  for  the  use  of  different  invertase  preparations.  The 
conditions  adopted  were  a  temperature  of  25°,  an  initial  sucrose  concen- 
tration of  10  g.  per  100  cc.,  and  a  hydrogen-ion  concentration  of  10~44 
to  10~4-5  secured  by  0.01  M  buffer  solution  of  acetic  acid  and  sodium 
acetate.  The  amounts  of  invertase  were  so  adjusted  in  each  experiment 
that  the  reaction  started  off  at  the  same  rate.  This  was  accomplished 
by  a  few  preliminary  experiments,  making  use  of  the  fact  noted  by  Nelson 
and  Vosburgh,1  that  the  velocity  of  inversion  is  directly  proportional  to 
the  concentration  of  the  enzyme.  The  extent  of  inversion  was  determined 
by  the  polariscopic  method.  That  this  method  is  justifiable  has  been 
established  by  Vosburgh2 

1  Nelson  and  Vosburgh,  J.  Am.  Chem.  Soc.,  39,  790  (1917). 

2  Vosburgh,  ibid.,  43,  219  (1921). 


Table  I  contains  the  results  of  10  experiments  with  4  different  invertase 
preparations.  These  preparations  were  all  obtained  from  yeast  by  modifi- 
cations of  the  method  of  Nelson  and  Born.  No  differences  in  the  method 
of  preparation  are  known  which  might  account  for  the  abnormality  of  No. 
3.  Further  description  of  the  method  of  preparation  will  be  found  under 
the  heading  "Experimental  Details." 

TABLE  I. 

DIFFERENCES  IN  INVERTASE  ACTION. 
Temp.,  25°.     Cone,  of  sucrose,  10  g.  per  100  cc.     Cone.  H+,  10~4'4  to  10 ~4-5  moles  per 

liter. 
A.     Normal  Invertase. 


Expt. 
Invertase    Preparation    No. 
Cc.  of  Invertase  per  100  cc. 
Initial    Rotation,    degrees. 

Time 

Bl.            B2.           B5.            B6. 
8.               8.               2.               2. 
1.530.       1.530.       7.141.      7.141. 
13.05.      13.04.      13.17.0     13.18.fl 

Change  in  rotation,  degrees. 

B9.           BIO. 

1.           1. 

6.080.      6.080. 
13.05.      13.04 

Mean 

Inverted 

Min. 

. 

%• 

5 

0 

.54      0. 

54 

0.53 

0.54 

0 

.52      0 

,51 

0.53 

3 

.15 

10 

1 

.07       1. 

07 

1.07 

1.07 

1 

.06       1 

,06 

1.07 

6 

.35 

15 

1 

.58       1. 

59 

1.58 

1.59 

1 

.58       1 

,57 

1.58 

9 

.38 

22 

2 

.33    .2. 

34 

2.32 

2.31 

2 

.31      2 

,31 

2.32 

13 

.77 

30 

3 

.12      3. 

14 

3.12 

3.12 

3 

.12      3 

,12 

3.12 

18 

.52 

60 

5 

.97      5. 

98 

5.97 

5.96 

5 

.98      5 

97 

5.97 

35 

.43 

90 

8 

.47      8. 

48 

8.46 

8.44 

8.50      8 

49 

8.47 

50 

.27 

120 

10 

.57     10. 

59 

10.55 

10.54 

10 

.58     10, 

59 

10.57 

62 

.73 

180 

13 

.52     13. 

53 

13.53 

13.50 

13 

.55     13. 

.53 

13.53 

80 

.30 

300 

15 

.93     15. 

93 

15.91 

15.93 

15 

.93     15, 

91 

15.92 

94 

.48 

2  to  4  days 

16 

.87     16. 

86 

16.85 

16.87 

16 

.85     16 

85 

16.86 

•• 

... 

B  .     Abnormal  Invertase  . 

Expt. 

Invertase    Preparation     No. 
Cc.  of  Invertase  per  100  cc. 
Initial    Rotation,    degrees. 

B12. 
3. 
1  .  905. 
13.05. 

B13. 
3. 
1  .  905. 
13.05. 

B14. 
3. 

1.905. 
13.05. 

B15. 
3. 
1.905. 
13.05. 

Mean. 

Time. 

Change  in 

rotation, 

degrees. 

Inverted 

A 

Min. 

15 

0.55 

0.54 

0.54 

0.54 

0 

.54 

3 

,20 

10 

1.07 

1.08 

1.07 

1.07 

1 

.07 

6 

35 

15 

1.59 

1.59 

1.59 

1.57 

1 

.59 

9 

,44 

22 

2.30 

2.31 

2.29 

2.30 

2 

.30 

13 

65 

30 

3.13 

3.11 

3.10 

3.08 

3 

.11 

18, 

46 

60 

5.92 

5.87 

5.88 

5.88 

5 

.89 

34 

96 

90 

8.33 

8.30 

8.32 

8.31 

8 

.32 

49, 

38 

120 

10.39 

10.34 

10.36 

10.35 

10 

.36 

61, 

48 

180 

13.27 

13.26 

13.30 

13.28 

13 

.28 

78. 

81 

300 

15.77 

15.73 

15.78 

15.81 

15.77 

93. 

58 

2  to  4  days 

16.85 

16.85 

16.85 

16.85 

16 

.85 

0  The  high  values  of  these  figures  are  due  to  the  fact  that  invertase  No.  2  itself 
had  an  unusually  high  rotation. 

It  will  be  noticed  that  the  results  indicate  that  in  6  experiments  with 
3  different  invertase  preparations  the  invertase  is  acting  alike  throughout 


9 

the  course  of  the  reaction.  The  results  of  the  last  4  experiments,  on  the 
other  hand,  while  agreeing  among  themselves,  do  not  agree  well  with  the 
other  results  beyond  about  the  first  20%  of  the  inversion,.  This  indicates 
that  invertase  preparation  No.  3  is  in  some  way  different  from  the  other 
preparations,  since  the  latter  part  of  the  reaction  is  noticeably  slower. 
These  results  therefore  show  that  not  all  preparations  of  invertase  have, 
under  a  given  set  of  conditions,  the  same  degree  of  activity.  It  was  thought 
at  first  that  this  retardation  might  be  due  to  spontaneous  destruction  of 
the  enzyme.  That  this  was  not  the  case  is  shown  by  the  results  of  ex- 
periment B15,  for  in  this  case  the  invertase  was  kept  in  the  thermostat 
for  5  hours  before  the  start  of  the  reaction.  It  has  been  shown  by  O'  Sul- 
livan and  Tompson3  that  invertase  suffers  spontaneous  destruction  less 
rapidly  in  the  presence  of  sucrose  than  in  its  absence.  Since  the  results 
of  Expt.  B15  indicate  no  loss  in  activity  of  the  invertase  in  5  hours  with- 
out the  presence  of  sucrose,  it  is  evident  that  the  difference  in  the  action 
of  invertase  preparation  No.  3  cannot  be  due  to  spontaneous  destruction 
of  the  enzyme.  Table  I  proves,  therefore,  that  while  there  seems  to  be 
a  normal  course  for  invertase  action,  there  are  also  exceptions  or  abnormal 
invertase  preparations. 

III.    Discussion  of  Equations  for  Invertase  Action. 

If  a  general  equation  for  normal  invertase  action  were  available,  it  would 
be  comparatively  easy  to  ascertain  from  experimental  data  whether  any 
given  preparation  were  normal  or  abnormal.  Nelson  and  Vosburgh1 
and  others  have  shown  that  the  rate  of  hydrolysis  of  cane  sugar  by  inver- 
tase is  not  proportional  to  the  concentration  of  the  substrate,  or,  in  other 
words,  the  reaction  does  not  obey  the  unimolecular  law, 

1  a 

*-7logo—  (1) 

where  k  is  the  velocity  coefficient,  /  time  in  minutes,  a  the  initial  cane 
sugar  concentration  and  x  the  amount  hydrolyzed. 

Henri4  proposed  an  empirical  equation  containing  only  one  constant. 

1        a  +  x 

k  ==lo- 


When  this  equation  was  applied  to  the  results  with  normal  invertase  given 
in  Table  IA,  decreasing  values  for  the  constant  were  obtained. 
Equations  of  the  form 

t  =  ki  log  —  —  +  fax.  (3) 

a—  x 


3  O'Sullivan  and  Tompson,  J.  Chem.  Soc.,  57,  834  (1890). 

4  Henri,   "Lois  generates  de  1'action  des  diastases,"  Hermann,  Paris,  1903,  p.  59. 


10 

were  deduced  by  Henri5  and  Bodenstein,6  by  Barendrecht,7  Michaelis  and 
Menten,8  and  Van  Slyke  and  Cullen.9  On  applying  the  method  of  least 
squares  to  the  present  results  (Table  IA)  to  determine  the  constants  for 
an  equation  of  this  type,  it  was  found  that  such  an  equation  would  not 
hold  satisfactorily  for  the  whole  course  of  the  reaction.  However,  by 
using  the  values  obtained  for  the  first  half  of  the  hydrolysis  only,  the  fol- 
lowing equation,  obtained  by  least  squares,  was  found  to  hold  for  the 
first  50%  of  the  hydrolysis. 

t  =  135.2  log  -^-   +  0.9724  p.  (4) 

±(j(j~—  p 

Here  t  is  the  number  of  minutes  required  for  p  per  cent,  of  the  sucrose  to 
be  inverted.  When  p  is  expressed  in  the  notation  of  Equation  1  it  is  equal 
to  100  x/a.  The  accuracy  with  which  the  equation  fits  the  results  may 
be  seen  from  the  following  figures. 


p.  t(calc.).  t(obs.).  p. 

3.15  4.94  5  18.52  30.0  30 

6.35  10.0  10  35.43  60.1  60 

9.37  14.9  15  50.27  89.9  90 

13.77  22.1  22 

By  considering  the  hydrolysis  of  sucrose  as  a  reversible  reaction,  uni- 
molecular  in  one  direction  and  bimolecular  in  the  other,  Visser10  deduced 
an  equation  which,  in  the  symbols  previously  used,  takes  the  form 

^=  *!(*-*)-*«**.  (5) 

eu 

On  applying  this  to  his  experiments  he  obtained  increasing  values  for  a 
quantity  which  should  theoretically  have  been  constant.  In  order  to 
correct  for  this  increase  he  introduced  a  factor  I  to  which  for  some  reason 
he  attributed  a  chemical  significance,  and  called  it  "the  intensity  of  the 
enzyme,"  giving  the  equation: 

^  =  [fc(a-*)  -***'!/.  (6) 

The  values  of  I  he  obtained  from  the  increasing  values  of  the  constant 
obtained  from  Equation  5,  and  he  found  they  could  be  expressed  by  the 
empirical  formula 

~ 


By  substituting  this  expression  in  Equation  6  and  integrating  he  obtained 

5  Op.  cit.,  p.  79. 

8  Bodenstein,    ibid.,    p.    92. 

7  Barendrecht,  Z.  physik.  Chem.,  49,  456  (1904). 

8  Michaelis  and  Menten,  Biochem.  Z.,  49,  333  (1913). 

9  Van  Slyke  and  Cullen,  /.  Biol.  Chem.,  19,  141  (1914). 

10  Visser,  Z.  physik.  Chem.,  52,  257  (1905). 


11 

a  complicated  equation  which  gave  constants  satisfactory  to  about  =*=  10%. 
Since  Hudson  li  has  shown  Visser's  theory  of  reversibility  to  be  unsound, 
no  attempt  was  made  to  apply  this  equation  to  the  present  results. 

Visser  also  proposed  a  simpler  equation  for  invertase  action,  obtained 
by  neglecting  the  reverse  reaction,  but  putting  the  same  factor  I  into  the 
unimolecular  equation. 


This  on  integration  becomes 


—  +  x(fia-x)  (9) 

a—  x 


Visser's  application  of  this  equation  to  his  own  experiments  gave  "con- 
stants" which  showed  an  extreme  variation  of  30%  (0.00108  to  0.00139) 
and  an  application  of  the  same  equation  to  the  experiments  of  Table  IA 
likewise  gave  increasing  values  for  the  constant. 
An  equation  of  similar  form, 

/  =  ki  log—  +  hr  +  fe*f,  (10) 

a—  x 

was  obtained  from  the  data  of  Table  IA  by  the  method  of  least  squares, 
but  did  not  fit  the  experimental  data  well  enough  to  be  of  any  use  in  the 
present  work. 

In  order  to  get  satisfactory  agreement  with  the  experimental  data,  it 
was  found  necessary  to  use  an  equation  containing  four  constants.  The 
following  equation  was  obtained  by  applying  the  method  of  least  squares 
to  the  mean  results  of  the  6  experiments  in  Table  IA. 

100 

t  =  222.  9  log  --  |-0.5890/>-0.001975£2-0.00002034£3.  (n) 

100  —  p 

The  applicability  of  this  equation  may  be  seen  from  the  following  figures  . 


TABLE  II. 

APPLICATION  OP  EMPIRICAL 

EQUATION. 

Inversion. 

P 

Time, 
/(calc.). 
Min. 

Time, 
/(obs.).                  n 
Min. 

x  io«.a 

3°15 

4.96 

5 

443 

6.35 

10.1 

10 

449 

9.38 

14.9 

15 

445 

13.77 

22.1 

22 

449 

18.52 

30.1 

30 

447 

35.43 

60.0 

60 

446 

50.27 

89.8 

90 

445 

62.73 

119.6 

120 

445 

80.30 

180.6 

180 

448 

94.48 

299.9 

300 

447 

Mean, 

446 

A.    d., 

0.36%. 

a  Meaning  of  n  explained  below. 


11  Hudson,   J.  Am.  Chem.  Soc.,  36,   1571    (1914). 


12 

IV.    An  Equation  for  Experiments  with  Different  Amounts  of  Invertase. 

Nelson  and  Vosburgh1  showed  that,  in  their  experiments  in  which  the 
initial  sucrose  concentration  was  constant,  the  time  required  for  a  given 
percentage  of  sucrose  to  be  inverted  was  inversely  proportional  to  the 
amount  of  invertase  used.  In  other  words,  letting  t  represent  the  time 
for  80%  inversion,  and  y  the  invertase  concentration,  in  experiments 
in  which  only  the  invertase  concentration  was  varied  they  found  the  pro- 
duct ty  to  be  constant.  In  another  series  of  experiments  with  a  different 
invertase  preparation  they  called  t  the  time  for  40%  inversion,  and  here 
again  ty  was  constant.  They  did  not,  however,  compare  the  times  for 
different  degrees  of  inversion  in  any  one  experiment,  say  t  for  40%  and  t 
for  80%  inversion,  because  they  did  not  know  the  law  governing  the  re- 
lationship between  the  time  and  the  percentage  of  inversion,  or,  mathe- 
matically, the  form  of  the  function,  t=i(p). 

It  is  obvious  that  one  may  plot  the  values  for  the  amounts  hydrolyzed 
in  various  times  against  the  times,  obtaining  curves  for  the  hydrolyses 
which  are  graphical  representations  of  the  function,  t  =  i(p).  This  was 
done  by  Michaelis  and  Davidsohn12  in  such  a  way  as  to  compare  the  form 
of  the  function  in  three  experiments  with  invertase  concentrations  in  the 
ratio  2:1: 0.4.  They  plotted  the  product  of  the  enzyme  concentration 
and  the  time,  ty,  against  the  change  in  rotation,  which  is  proportional  to 
the  percentage  inverted,  p.  They  claimed  that  the  points  all  fell  on  a 
smooth  curve,  and  that  therefore  the  form  of  the  hydrolysis  curve  was 
independent  of  the  amount  of  enzyme.  However,  only  3  experiments 
were  given  of  which  one  was  represented  by  only  2  points.  Moreover, 
their  whole  curve  did  not  appear  to  extend  much  beyond  the  first  half  of 
the  inversion,  and  in  addition  several  of  their  points  did  not  fall  on  the 
curve,  even  on  the  small  scale  used  in  their  printed  article.  Because  of 
these  deficiencies,  and  because  the  shape  of  the  curve  is  a  fundamental 
point  in  the  present  investigation,  it  seemed  best  to  amplify  their  data 
by  the  use  of  the  more  extensive  experiments  of  Nelson  and  Vosburgh. 

Accordingly  the  results  of  the  latter  were  plotted  in  a  similar  way  on  a 
large  scale.  The  curves  were  brought  together  at  one  point  by  using  a 
different  time  scale  for  each  experiment.  When  the  remainder  of  each 
curve  was  plotted  on  this  new  scale,  it  was  found  that  the  curves  for  experi- 
ments with  the  same  initial  sucrose  concentration  did  superimpose,  falling 
on  a  single  smooth  curve.  Thus  the  conclusion  drawn  by  Michaelis  and 
Davidsohn  was  more  firmly  established  by  the  results  of  Expts.  6,  7,  8,  9, 
10,  22  and  23  of  Nelson  and  Vosburgh,  each  experiment  including  at  least 
6  samples  and  extending  over  95%  or  more  of  the  inversion.  This  means 
that  the  function,  t  =  f  (p),  representing  a  single  experiment,  can  be  general- 
ized as  nt  =  J?  (p)  for  experiments  with  varying  amounts  of  invertase^ 
12  Michaelis  and  Davidsohn,  Biochem.  Z.,  35,  386  (1911). 


13 

Here  n  is  a  constant  in  any  one  experiment,  but  varies  in  different  experi- 
ments, being  proportional  to  the  amount  of  effective  invertase.  Moreover 
the  form  of  the  function  nt  —  F  (p)  is,  within  the  limits  of  these  experi- 
ments, independent  of  the  amount  of  invertase  or  of  the  rate  of  the  hy- 
drolysis. 

A  more  exact  verification  of  this  relationship  was  obtained  by  the  use 
of  Equation  11,  which  gives  a  definite  form  to  the  function,  *  =  f  (p),  for 
one  particular  invertase  concentration.  In  order  to  make  this  equation 
generally  applicable  to  experiments  with  other  invertase  concentrations, 
the  coefficient  of  the  logarithmic  term  was  placed  equal  to  l/n  and  factored 
out,  giving 

+  0.002642^-0.  000008860/>2-0.0000001034£3]  .      (12) 


i 
n  100  —  p 

If  it  is  generally  true  that  the  times  for  any  given  percentage  of  inversion 
are  inversely  proportional  to  the  amounts  of  invertase  used,  then  Equa- 
tion 12  gives  a  definite  form  to  the  function,  t  =  i  (p),  for  any  invertase 
concentration.  Whether  or  not  this  is  the  case  can  be  tested  by  substi- 
tuting in  Equation  12  the  experimental  values  for  p  and  /,  and  calculating 
the  values  of  n.  If  the  latter  are  constant,  the  equation  applies  and  the 
general  law  holds,  and  the  values  of  n  should  be  directly  proportional  to 
the  amounts  of  active  invertase  present. 

To  recapitulate,  we  have,  if  this  is  true,  first  an  empirical  relation  be- 
tween time  and  percentage  inverted  which  holds  for  experiments  in  which 
different  amounts  of  invertase  are  used;  and,  second,  we-have  in  the  value 
of  n  a  relative  measure  of  the  amount  of  the  effective  invertase. 

In  order  to  decide  whether  or  not  Equation  12  applies  to  a  given  experi- 
ment, it  is  necessary  to  decide  whether  or  not  the  values  of  n  are  constant. 
The  values  of  n  for  the  experiments  of  Table  IA,  from  which  the  equation 
was  derived,  are  given  in  the  last  column  of  Table  II.  The  average  de- 
viation from  the  mean,  0.36%,  is  an  indication  of  the  extent  to  which  the 
equation  fits  these  original  experiments.  To  determine  about  what  magni- 
tude of  deviation  from  the  mean  might  be  due  to  experimental  error  in 
applying  the  equation  to  other  experiments,  the  following  calculations 
were  made. 

From  the  agreement  of  duplicate  experiments  in  Table  I  and  subsequent 
experiments,  the  average  error  in  determining  any  change  in  rotation  was 
estimated  as  0.02°.  To  determine  what  error  in  n  could  be  caused  by  such 
an  error,  the  value  0.02  °  was  added  to  all  the  changes  in  rotation  of  Table 
IA,  and  the  values  of  n  recalculated,  with  the  results  shown  in  Table  III. 

Evidently  the  form  of  the  relationship  is  such  that  errors  are  magnified 
in  the  values  of  n  calculated  from  the  data  on  the  early  part  of  the  hy- 
drolysis. Since  in  all  the  experiments  of  the  present  work  except  those 
of  Table  I  the  first  sample  was  taken  at  about  10%  inversion,  while  the 


14 

TABLE  III. 
EFFECT  OF  ASSUMED  ERROR  OP  0.02°. 

P  +  error.  t.         10*  (n  +  error).    108  (n  true  Error  in      Dev.  from 

values).       10*M.    true  mean. 

3.26  5  458  443  15  12 

6.47  10  457  449  8  11 

9.50  15  450  445  5  4 

13.89  22  453  449  4  7 

18.64  30  450  447  3  4 

35.55  60  448  446  2  2 

50.39  90    .  446  445  1  0 

62.85  120  446  445  1  0 

80.42  180  450  448  2  4 

94.60  300  450  447  3  4 

Mean,  4. 4  =  0.99%. 

Mean,4.8  =  1.08%. 

other  7  samples  were  distributed  about  as  before,  it  was  decided  that 
a  fairer  measure  of  the  average  error  in  n  would  be  given  by  the  mean  of 
the  last  8  of  the  above  values.  This  gives  an  average  deviation  of 
0.59%  from  the  individual  values  of  n,  or  of  0.70%  from  the  mean  value 
of  n  as  the  deviation  caused  by  an  error  of  0.02°  in  the  value  of  each  change 
in  rotation.  Hence  it  may  fairly  be  decided  that  any  experiment  giving 
an  average  deviation  from  the  mean  of  0.7%  or  less  is  fitted  by  the  equation, 
and  its  curve  has  the  same  shape  or  the  function,  nt  =  T?  (p),  has  the  same 
form  as  in  the  case  of  the  original  experiments  of  Table  IA. 

Since  the  results  of  Nelson  and  Vosburgh  were  available,  including  ex- 
periments in  which  the  concentration  of  invertase  was  varied,  it  was  thought 
that  these  results  might  well  be  used  as  a  test  of  the  general  applicability 
of  Equation  12.  Accordingly  Table  IV  was  prepared  by  using  those  of 
their  experiments  in  which  the  initial  sucrose  concentration  was  10  g.  per 
100  cc. 

In  the  last  three  of  these  experiments  the  average  deviation  from  the 
mean  of  the  values  of  n  is  below  the  value  0.7%.  As  has  been  already 
pointed  out,  this  deviation  might  be  caused  by  experimental  error,  and 
accordingly  the  equation  fits  these  three  experiments  satisfactorily.  In 
Expts.  6,  8,  and  9  the  first  sample  was  taken  before  the  inversion  was  10% 
complete.  Now  it  has  been  already  pointed  out  that  in  this  part  of  the 
inversion  a  small  experimental  error  may  cau^se  a  large  error  in  the  value 
of  n.  Accordingly  for  these  experiments  the  mean  of  the  remaining  values 
of  n  was  calculated,  omitting  the  first,  and  the  average  deviations  were 
found  to  be  0.64%,  0.40%,  and  0.10%  for  Expts.  6,  8  and  9,  respectively. 
Therefore  the  equation  really  does  fit  6  of  the  7  experiments  in  Table  IV, 
and  it  may  be  concluded  with  more  certainty  than  before  that  the  shape 
of  the  hydrolysis  curve  or  the  form  of  the  function,  n£  =  F  (p),  isindepend- 


15 


TABLE  IV. 

EFFECT  OF  VARYING  AMOUNTS  OF  INVERTASE.     (EXPERIMENTS  OF  NELSON  AND  Vos- 

BURGH.) 

Initial  sucrose  concentration,  10  g.  per  100  cc.     Hydrogen-ion  concentration,  3.2  X 
10 ~5  to  2.1    X   10 ~6  moles  per  liter.     Temperature,  37°.     Invertase  preparation  A 
used  in  Expts.  6  to  10,  Preparation  B  in  Expts.  22  and  23. 


Inv.  per    Time. 
Expt.       100.            /. 
Cc.         Min. 

Amt.  in- 
verted, 
P,%. 

«xio». 

66             14 

8.32 

422 

30 

17.92 

433 

70 

39.85 

437 

120 

61.90 

437 

185 

80.59 

439 

320 

94.97 

431 

Mean, 

433 

Av 

.  dev.,  1  . 

04%. 

8        4          20 

8.31 

295 

45 

18.69 

301 

105 

41.17 

302 

175 

62.11 

301 

265 

80.09 

303 

450 

94.85 

305 

Mean, 

301 

Av. 

dev.,  0. 

73%. 

10        2          50 

10.01 

143 

100 

20.14 

146 

221 

42.09 

147 

315 

56.10 

146 

345 

60.04 

146 

570 

81.60 

147 

1365 

98.06 

(131)° 

Mean, 

146 

Av.  dev.,  0 

.57%. 

23        2           14 

10.34 

526 

28 

20.49 

533 

60 

41.81 

538 

100 

62.62 

533 

156 

81.70 

537 

280 

95.70 

(517)° 

Mean, 

533 

Inv.  per 
Expt.      100. 
Cc. 

Time      Amt.  in- 
t.           verted. 
Min.         p,  %. 

nX10». 

7        5 

22 

11.08 

360 

40 

20.15 

366 

90 

43.21 

372 

138 

60.98 

372 

215 

80.30 

375 

373 

95  '.04 

370 

Mean 

,   369 

Av 

.dev.,  1, 

14%. 

9        3 

33 

9.57 

206 

70 

20.49 

213 

150 

41.50 

213 

250 

62.44 

212 

376 

80.09 

213 

660 

95.28 

213 

Mean 

,    212 

Av. 

dev.,  0. 

80%. 

22         1 

30 

10.91 

259 

60 

21.50 

261 

122 

41.21 

260 

200 

61.49 

260 

305 

79.65 

260 

600 

96.08 

(248)  a 

Mean, 

260 

Av.  dev.,  0.17%. 


Av.  dev.,  0.60%. 

a  These  values  are  for  points  beyond  the  limit  of  p,  95%,  for  which  the  equation 
was  derived,  and  hence  were  not  used  in  taking  the  mean. 

ent  of  the  invertase  concentration,  and  that  Equation  12  gives  a  definite 
form  to  this  function,  F(^). 

In  view  of  the  fact  that  the  extreme  variation  in  the  invertase  concen- 
tration in  these  experiments  was  from  6  cc.  to  2  cc.  or  in  the  ratio  3:1,  while 
the  range  covered  by  the  rather  unsatisfactory  experiments  of  Michaelis 
and  Davidsohn  was  5 :1,  it  seemed  best  to  try  the  effect  of  a  wider  variation 


16 


in  invertase  concentration  on  the  shape  of  the  curve.  The  highest  con- 
centration used  was  selected  so  as  to  make  the  hydrolysis  as  rapid  as  possi- 
ble without  causing  error  in  the  timing  of  samples,  and  the  lowest  concen- 
tration was  such  that  the  first  and  last  samples  could  just  conveniently 
be  taken  on  the  same  day.  In  view  of  the  difficulty  encountered  in  a  pre- 
vious investigation13  in  obtaining  reproducible  results  with  very  dilute 
invertase  solutions,  it  seemed  unwise  to  attempt  to  study  slower  reactions 
than  this.  The  results  of  the  experiments  with  the  extreme  invertase 
concentrations  used,  in  the  ratio  12:1,  are  given  in  Table  V. 

TABLE  V. 

EXTREME  CHANGES  IN  INVERTASE  CONCENTRATION. 


Expts.  B60  and  B61. 
6  cc.  of  Invertase  8  per  100  cc. 


Expt.  B62. 
0 . 5  cc.  of  Invertase  8  per  100  cc. 


Time, 
t. 
Min. 

0 
5 

Rotation, 
B60.                B61. 
Degrees. 

13.09           13.09 
11.11           11.11 

Amt. 
inverted,     nXlO*. 
P,  %• 

11.75        168 

Time. 
t. 

Min. 

0 

60 

Rotation, 
degrees. 

13.04 
11.11 

Amt. 
inverted,      nX10B. 
P,  %• 

11.45 

136 

10 

9.24 

9.25 

22.85 

167 

120 

9.28 

22.31 

136 

15 

7.50 

7.51 

33,18 

166 

180 

7.58 

32.40 

135 

21 

5.57 

5.58 

44.63 

166 

252 

5.68 

43.68 

135 

28 

3.59 

3.59 

56.38 

165 

336 

3.76 

55.07 

134 

37 

1.49 

1.49 

68.84 

166 

444 

1.70 

67.30 

133 

52 

-0.93 

-0.94 

83.26 

168 

624 

-0.70 

81.54 

134 

70 

-2.43 

-2.43 

92.11 

170 

840 

-2.26 

90.80 

134 

1-7  days 

-3.76 

-3.76 

Mean, 

167 

11  days 

-3.81 

Mean, 

135 

Av.dev.,     0.75%  Av.  dev.,0.65% 

The  values  of  n  are  sufficiently  constant  so  that  the  equation  may  be 
said  to  hold  for  these  concentrations. 

If  the  time  for  any  given  percentage  of  in  version  is  inversely  proportional 
to  the  concentration  of  invertase,  the  value  of  n  divided  by  the  number 
of  cubic  centimeters  of  invertase  used  per  100  cc.  of  solution  should  be  a 
constant  for  any  given  invertase  preparation.  For  Expts.  Bl  and  B2 
(Table  IA)  this  value  is  0.00292;  for  Vosburgh  and  Nelson's  Expt.  IB 
(Table  VI),  it  is  0.00290;  for  B60  and  B61,  0.00278;  and  for  B62,  0.00270. 
These  experiments  were  all  made  with  Invertase  8.  The  difference  be- 
tween the  former  two  and  the  latter  two  values  is  due  to  slow  deterioration 
of  the  invertase,  even  when  kept  in  the  ice-box,  for  a  period  of  8  months 
had  elapsed  between  the  two  sets  of  experiments.  The  smaller  difference 
between  the  latter  two  values  can  hardly  be  so  explained,  as  the  experi- 
ments were  run  on  successive  days,  but  must  be  taken  to  mean  that  for 
this  range  of  concentrations  the  effective  activity  of  the  invertase  is  not 
strictly  proportional  to  the  actual  concentration  used.  However,  since 
the  equation  applies  equally  well  in  both  cases,  it  may  be  stated  as  a  fact 
13  Nelson  and  Hitchcock,  "The  Activity  of  Adsorbed  Invertase,"  J.  Am.  Chem. 
Soc.,  43,  1956  (1921). 


17 


that  over  this  range  Q£  invertase  concentrations  (12: 1)  the  form  of  the 
function,  wZ  =  F(£),  is  the  same  and  is  expressed  by  Equation  12,  while 
the  value  of  n  represents  accurately  the  true  activity  of  the  invertase 
even  better  than  its  relative  concentration. 

V.    Effect  of  Temperature. 

Since  the  experiments  of  Nelson  and  Vosburgh  were  carried  out  at  37° 
while  the  present  experiments  were  run  at  25°,  it  seemed  that  the  effect 
of  temperature  differences  in  any  two  experiments  might  be  constant  for 
all  stages  of  the  reaction.  Inasmuch  as  some  experiments  on  the  course 
of  the  hydrolysis  at  various  temperatures  had  recently  been  made  in  this 

TABLE  VI. 

EFFECT  OF  TEMPERATURE.     (EXPERIMENTS  OF  VOSBURGH  AND  NELSON.) 
Initial  sucrose  concentration,  10  g.  per  100  cc.     Hydrogen-ion  concentration,  4 . 4  X  10  ~5 
to  4.0  X  10 ~5  moles  per  liter.     Invertase  preparation  No.  8,  1  cc.  per  100  cc. 


Expt.  Temp. 
0  C 

Time, 
/. 
Min. 

Amt. 
inverted, 
P,  %• 

«X105.     Expt.    Temp. 
0  C. 

Time, 
t. 
Min. 

Amt. 
inverted, 

nXlO 

11B      15 

21 

5.22 

175         15B      20 

16 

5.04 

222 

63 

14.54 

166 

38 

11.87 

223 

110 

24.39 

163 

65 

19.82 

222 

162 

34.72 

162 

120 

34.90 

220 

250 

50.45 

161 

155 

43.68 

219 

350 

65.04 

161 

190 

51.40 

217 

441 

75.07 

161 

254 

63.92 

216 

586 

85.88 

162 

320 

74.18 

217 

Mean, 

164 

420 

84.87 

218 

Av, 

,  dev.,  2.07%. 

Mean, 

219 

Av. 

dev.,  0.96%. 

IB      25 

15 

6.17 

290          5B     30 

9 

4.93 

381 

36 

14.60 

292 

29 

15.07 

374 

63 

24.80 

289 

50 

25.22 

371 

105 

39.70 

290 

71 

35.05 

373 

165 

57.39 

287 

107 

49.79 

370 

235 

73.24 

289 

153 

65.34 

370 

360 

88.84 

290 

190 

75.07 

373 

Mean 

,  290 

246 

84.93 

374 

Av 

.  dev.,  0. 

34%. 

Mean, 

373. 

Av.  dev.,  0.60%. 


7B      35 


8 

24 

42 

60 

90 

120 

155 

195 


5.46 
15.76 
26.59 
36.91 
52.11 
64.63 
76.02 
84.93 


482 
473 
467 
467 
465 
464 
467 
471 


Mean,  469 
Av.  dev.,  0.91%. 


18 

laboratory  by  Vosburgh  and  Nelson,14  it  seemed  inadvisable  to  repeat 
this  work.  Accordingly  the  effect  of  temperature  on  the  shape  of  the 
hydrolysis  curve  was  tested  by  applying  Equation  12  to  these  experiments, 
with  the  results  shown  in  Table  VI. 

In  all  of  these  experiments  the  first  sample  was  taken  at  a  point  con- 
siderably below  10%  inversion.  Therefore,  in  order  to  compare  the  average 
deviation  with  that  which  might  be  due  to  experimental  error,  the  values 
obtained  from  the  first  sample  should  be  omitted  in  taking  the  mean. 
If  this  is  done  the  values  for  the  average  deviation  are  as  follows:  Kxpt. 
11B,  0.68%;  15B,  0.91%;  IB,  0.34%;  5B,  0.43%;  and  7B,  0.56%.  All 
of  these  except  that  for  Expt.  15B  are  less  than  0.7%,  and  accordingly 
Equation  12  fits  these  experiments  fairly  well.  This  establishes  for  the 
first  time  the  fact  that  temperature  differences,  at  least  between  15°  and 
35°,  have  no  effect  on  the  shape  of  the  hydrolysis  curve  or  the  form  of 
the  function,  nt  =  'P  (p).  In  other  words,  an  increase  in  the  temperature 
has  the  same  quantitative  effect  as  an  increase  in  the  amount  of  the  inver- 
tase  used. 

VI.    Effect  of  Hydrogen-ion  Concentration. 

In  his  classical  study  of  the  effect  of  hydrogen -ion  concentration  on  in- 
vertase  action,  Sorensen15  found  that  the  velocity  coefficient  k  calculated 
according  to  the  unimolecular  law  in  the  form 

1       a—xi 

k  = In 

h  —  h     a—xz 

increased  considerably  as  the  reaction  progressed  in  nearly  neutral  solu- 
tions (CH+  =  10~6  to  10~7),  increased  less  around  the  optimum  (CH+  = 
10 ~4  to  10 ~5),  remained  constant  in  slightly  more  acid  solutions  (CH+  = 
1.2X10"4),  and  decreased  in  still  more  acid  solutions  (CH+  =  2.1X10~4). 
This  means  that  the  shape  of  the  hydrolysis  curve  or  the  form  of  the  func- 
tion nt  =  3?  (p)  was  not  the  same,  in  his  experiments,  for  different  hydrogen- 
ion  concentrations.  Michaelis  and  Davidsohn12  have  pointed  out  that 
this  variation  may  be  explained  in  part  by  destruction  of  the  invertase 
in  the  more  acid  solutions  at  the  rather  high  temperature,  52°,  at  which 
Sorensen  carried  on  his  experiments.  By  using  a  lower  temperature, 
22.3°,  they  obtained  values  of  k  calculated  from  the  equation 

k  -  i  log  JL 

t          a-x 

which  increased  in  experiments  at  hydrogen-ion  concentrations  less  than 
3.0X10"3,  where  they  remained  constant.  Nelson  and  Vosburgh,1  on 
the  other  hand,  found  that  at  37  °  the  values  of  k  increased  in  experiments 

14  Vosburgh  and  Nelson,  "The  Temperature  Coefficient  of  Invertase  Action,"  (to 
be  published  later). 

15  Sorensen,  ^Biochem.  Z.,  21,  131-304  (1909);    also  Compt.  rend.  Lab.  Carlsberg, 
8,    1   (1909). 


19 

at  the  optimum  hydrogen-ion  concentration,  3.2X10"6,  but  increased 
more  slowly  or  remained  constant  at  3. 2X10 ~6.  They  noticed,  however, 
that  there  were  some  changes  in  the  hydrogen-ion  concentration  during 
the  latter  half  of  the  inversion  at  about  3.2X10"6. 

The  equation  of  the  present  work  will  not  fit  experiments  in  which  the 
values  of  the  unimolecular  "£"  are  constant  or  decrease,  because  it  was 
derived  for  experiments  for  which  the  unimolecular  '"k"  increased.  In 
order  to  test  the  effect  of  hydrogen-ion  concentration  on  the  shape  of  the 
curve  the  equation  was  applied  to  some  recent  experiments  of  Vosburgh 
and  Nelson  (to  be  published  later)  in  which  the  hydrogen-ion  concentra- 
tion was  held  constant  at  10  ~6  moles  per  liter  by  means  of  citrate  buffers 
and  the  improved  procedure  recommended  by  Vosburgh16  was  used. 
These  results  are  given  in  Table  VII. 


(EXPERIMENTS  OF  Vos- 


VII. 

EFFECT  OF  A  DIFFERENT  HYDROGEN-ION  CONCENTRATION. 

BURGH  AND  NELSON.) 

Initial  sucrose  concentration,  10  g.  per  100  cc.     Hydrogen-ion  concentration,  1 . 10  X 10  ~6 
to  1 . 13  X  10  ~6  moles    per  liter.     Invertase  preparation  No.  8,  1  cc.  per  100  cc. 


Expt.  Temp. 
0  C. 

Time, 
t. 
Min. 

Amt. 
inverted, 

P,%. 

nXlO'. 

Time 
Expt.  Temp.        t. 
0  C.       Min. 

,         Amt. 
inverted, 
P,  %- 

nX10«. 

13B      15 

23 

4.99 

153 

2B      25        30 

11,10 

264 

75 

15.43 

148 

55 

19.76 

261 

126 

25.34 

148 

80 

28.13 

261 

183 

35.67 

148 

101 

34.84 

260 

282 

51.57 

147 

138 

45.58 

258 

390 

65.  .46 

146 

217 

64.87 

258 

490 

75.43 

146 

350 

84.69 

261 

642 

85.52 

146 

Mean, 

260 

Mean, 
Av.  dev.,  1. 

148 

01%. 

Av.  dev.,  0 

.62%. 

9B      35 

10 

5.88 

415 

26 

15.01 

415 

44 

24.75 

413 

64 

35.10 

414 

98 

50.56 

412 

135 

64.45 

411 

171 

74.96 

413 

225 

85.52 

416 

Mean, 

414 

Av.  dev.,  0.34%. 

Except  for  the  first  value  in  Expt.  13B,  the  deviation  of  which  may  be 
due  to  a  slight  experimental  error,  as  has  been  already  pointed  out,  the 
constancy  of  n  is  very  satisfactory.  This  means  that  at  a  hydrogen-ion 
concentration  of  10  ~6  moles  per  liter  the  curve  has  the  same  shape  or  the 
16  Vosburgh,  "Some  Errors  in  the  Study  of  Invertase  Action,"  /.  Am.  Chem.  Soc., 
43,  1693  (1921). 


20    • 

function  nt  =  F(p)  has  the  same  form  as  at  the  optimum  hydrogen-ion 
concentration.  The  differences  found  by  Nelson  and  Vosburgh1  at  CH  + 
3!2X10~6  must  be  ascribed  to  changes  in  the  hydrogen-ion  concentration 
or  in  the  amount  of  active  invertase  due  to  the  use  of  hydrochloric  acid 
without  buffer.  The  nature  of  the  buffer,  however,  does  not  seem  to 
affect  the  shape  of  the  curve,  for  the  experiments  of  the  present  work  were 
made  with  a  0.01  M  buffer  mixture  of  acetic  acid  and  sodium  acetate, 
while  the  experiments  of  Vosburgh  and  Nelson  quoted  in  Tables  VI  and 
VII  were  made  with  a  similar  concentration  of  citric  acid  and  sodium 
citrate.  Very  recently  the  range  for  which  the  equation  holds  has  been 
extended  to  CH+  3.2X10"7  by  some  experiments  of  Nelson  and  Bloom- 
field  (not  yet  published).  These  results  mean  that  within  the  limits  given 
changes  in  hydrogen-ion  concentration  affect  the  activity  of  the  invertase 
in  just  the  same  way  as  changes  in  temperature  or  in  the  amount  of  in- 
vertase used;  either  there  is  actually  a  change  in  the  amount  of  the  active 
substance  present  throughout  the  experiment  or  else  the  activity  of  the 
amount  present  is  uniformly  reduced  or  increased  by  the  change  and  re- 
mains constant  throughout  the  experiment. 

VII.    A  Criterion  of  Normal  Invertase  Action. 

Above,  in  Part  II  of  this  paper,  experiments  were  given  which  showed 
that  not  all  invertase  preparations  impart  the  same  shape  to  the  hydrolysis 
curve.  Equation  12  was  made  to  fit  the  experiments  in  Table  IA,  made 
with  invertase  preparations  which  were  classified  as  normal.  Accordingly 
it  seemed  probable  that  it  would  not  fit  the  experiments  in  Table  IB,  and 
hence  might  be  used  as  a  means  of  distinguishing  between  normal  and 

TABLE  VIII. 
APPLICATION  OP  THE  EQUATION  AS  A  CRITERION  OF  NORMAL  INVERTASE  ACTION. 

Expts.  B 12-15.  Expts.  B17  and  B18. 

1 .905  cc.  of  Invertase  3  per  100  cc.  10.45cc.  of  Invertase  6  per   100  cc. 


Time 
Min. 

Amt. 
inverted, 

P,  %• 

nX10«. 

Time, 
t. 
Min. 

Rotation, 
B17.                      B18. 
Degrees. 

Amt. 
inverted, 
P.%. 

nXlO*. 

0 

0 

0 

13.15                  13.15 

0 

5 

3.20 

450 

15 

11.47              11.46 

10.03 

476 

10 

6.35 

449 

30 

9.88                9.88 

19.41 

470 

15 

9.44 

448 

50 

7.90                7.90 

31.16 

466 

22 

13.65 

445 

70 

6.10                6.10 

41.84 

461 

30 

18.46 

446 

90 

4.52                4.49 

51.34 

457 

60 

34.96 

440 

115 

2.75 

61.72 

454 

90 

49.38 

436 

140 

1.35                1.32 

70.15 

451 

120 

61.48 

433 

180 

-0.36             -0.40 

80.30 

448 

180 

78.81 

431 

240 

-1.95             -1.96 

89.67 

449 

300 

93.59 

426 

300 

-2.74             -2.74 

94.30 

443 

Mean, 

440 

2  to  7  days 

-3.71             -3.71 

Mean, 

457 

Av.  dev.,  1 

.4%. 

Av.  dev., 

1.9%. 

,  21 

abnormal  invertase  preparations.  Equation  12,  therefore,  was  applied 
to  the  results  of  Table  IB,  and  also  to  experiments  with  two  other  invertase 
preparations,  Nos.  6  and  7,  with  the  results  shown  in  Table  VIII. 

Expts.  B20  and  B21. 
3.60  cc.  of  Invertase  7  per  100  cc. 

Time,  Rotation,  Amt.- 

/.  B20.  B21.  inverted,  n  X  10«. 

Min.  Degrees.  p,  %. 

0  13.07  13.08  0 

15  11.47  11.47  9.55  453 

30  9.89  9.91  18.87  456 

50  7.94       .  7.96  30.45  454 

70  6.17  6.16  41.00  451 

90  4.53  4.54  50.68  450 

117  2.64  2.66  61.90  448 

140  1.29  1.33  69.85  448 

180  -0.49  -0.43  80.36  449 

240  -2.06  -2.06  89.85  452 

300  -2.85  -2.81  94.42  446 

2  to  7  days         -3.78  -3.78                            Mean,    450 

Av.   dev.,  0.56%.    - 

It  will  be  noticed  in  Expts.  B 12-15,  Table  VIII,  that  for  those  points 
where  the  data  of  Table  IB  coincided  with  those  of  Table  I  A,  or  up  to 
20%  of  the  inversion,  the  values  of  n  are  fairly  constant,  even  for  abnormal 
invertase.  The  abnormality,  however,  shows  up  later  in  the  decreasing 
values  of  n,  and  is  indicated  by  the  larger  values  of  the  average  deviation 
of  a  single  value  of  n  from  the  mean,  which  is  well  above  0.7%  for  the  ex- 
periments with  Invertase  3.  Expts.  B17  and  B18  indicate  that  Invertase 
6  is  also  an  abnormal  invertase  preparation,  since  the  values  of  n  decrease 
and  the  average  deviation  is  well  above  0.7%.  Invertase  7,  on  the  other 
hand,  is  a  normal  invertase  preparation,  as  is  shown  by  Expts.  B20  and 
B21,  since  the  values  of  n  exhibit  satisfactory  constancy.  These  experi- 
ments indicate  that  Equation  12  may  be  used  as  a  criterion  of  normal 
invertase  action.  In  order  to  decide  whether  invertase  preparations  are 
normal  or  abnormal,  then,  it  is  no  longer  necessary  to  use  them  at  initially 
equivalent  effective  concentrations,  but  the  experiments  may  be  made  with 
any  concentration,  at  least  within  the  limits  of  the  experiments  in  Table 
V.  If  the  average  deviation  of  the  values  of  n  is  under  0.7%,  the  invertase 
preparation  may  be  classified  as  normal;  if  the  values  of  n  decrease  and 
the  average  deviation  is  much  over  0.7%,  then  the  invertase  preparation 
is  abnormal. 

VIII.     Attempts  to  Make  the  Abnormal  Invertase  Act  Normally. 

There  were  no  known  differences  in  the  method  used  in  obtaining  the 
normal  and  abnormal  invertase  preparations.  However,  it  was  deemed 
advisable  to  find  out  whether  the  abnormality  could  be  due  to  some  im- 


22 


purity  which  might  be  removed  by  further  dialysis.  Accordingly  a  sample 
of  Invertase  6  was  dialyzed  for  3  days  more  in  a  collodion  bag  against 
running  tap  water.  During  the  dialysis  its  volume  was  about  doubled 
and  its  activity  decreased  by  about  x/2  on  that  account  ;  this  was  designated 
as  Invertase  6B.  To  avoid  this  loss  in  activity,  a  sample  of  Invertase  3 
was  concentrated  by  evaporation  in  a  collodion  bag  by  fanning  at  room 
temperature17  until  it  had  lost  about  half  its  volume,  and  then  dialyzed 
for  4  days,  when  it  had  regained  about  its  original  volume  ;  this  was  desig- 
nated as  Invertase  3B.  The  results  of  experiments  with  these  dialyzed 
preparations  are  given  in  Table  IX. 


TABLE  IX. 
EFFECT  OF  DIALYSIS  ON  ABNORMAL  INVERTASE. 


Expt.  B22. 
16  cc.  of  Invertase  6B  per  100  cc. 

Time,  Amt. 

inverted, 


Expt.  B24. 


Min. 

Rotation, 
degrees. 

0 

13.10 

15 

11.41 

30 

9.78 

50 

7.74 

70 

5.89 

90 

4.24 

115 

2.53 

140 

1.10 

180 

-0.58 

240 

-2.08 

300 

-2.83 

nXlO*. 


Time, 

t. 
Min. 


Rotation, 
degrees. 


:  SB  per 

100  cc. 

Amt. 

averted. 

nX10«. 

0 

9.55 

453 

18.75 

453 

35.43 

446 

49.97 

442 

61.72 

435 

78.58 

429 

87.95 

422 

92.94 

412 

Mean, 

437 

0  ...  0  13.05 

10.03  476  15  11.44 

19.70  477  30  9.89 

31.81  476  60  7.08 

42.79  473  90  4.63 

52.58  470  120  2.65 

62.73  464  180  -0.19 

71.22  462  240  -1.77 

81.19  459  300  -2.61 

90.09  456  4  days  -3.80 

94.54  449                                                   Av.  dev.,  2.75%. 

Mean,  466 

Av.  dev.,  1.76%. 

The  decrease  in  the  values  of  n  and  the  large  average  deviations  show  that 
the  invertase  was  still  abnormal.. 

Since  the  abnormality  could  not  be  removed  by  purification  by  dialysis, 
it  was  thought  that  it  might  be  due  to  the  absence  of  some  substance  con- 
tained in  the  normal  invertase.  A  sample  of  Invertase  8  was  inactivated 
by  boiling,  and  was  proved  to  be  totally  inactive  by  the  absence  of  any 
action  on  sugar  solutions.  Experiments  were  then  conducted  in  which 
the  solutions  contained  10  cc.  of  this  inactive  invertase  per  100  cc.  in  addi- 
tion to  the  abnormal  invertase  under  investigation.  The  results  are  given 
in  Table  X. 

The  figures  in  Table  X  indicate  that  the  presence  of  boiled  normal  in- 
vertase caused  preparation  No.  3  to  act  normally,  giving  constant  values 
of  n,  while  it  was  practically  without  effect  on  preparation  No.  6.  •  This 
apparently  means  that  there  are  different  kinds  of  abnormality  in  different 
invertase  preparations. 

17  Kober,  J.  Am.  Chem.  Soc.,  39,  944  (1917). 


23 


TABLE  X. 
EFFECT  OF  BOILED  NORMAL  INVERTASE  ON  THE  ACTION  OF  ABNORMAL  INVERTASE. 


Expt. 

B25. 

10  cc. 

of  boiled  Invertase  8  and 

1.905cc. 

of  Invertase  3 

per  100  cc. 

Time, 

Amt. 

Rotation, 

inverted, 

«X10». 

Min. 

degrees. 

P,  %• 

0 

13.17 

0 

.  . 

15 

11.61 

9.26 

439 

30 

10.10 

18.22 

440 

60 

7.31 

34.78 

437 

90 

4.85 

49.38 

436 

120 

2.78 

61.66 

434 

180 

-0.19 

79.29 

437 

240 

-1.85 

89.14 

440 

300 

-2.68 

94.07 

437 

3  days 

-3.68 

Mean,   437 

•  Av.  dev., 

0.34%. 

Expt.   B26. 
10  cc.  of  boiled  Invertase  8  and  1  .943  cc. 

of  Invertase  3 

perlOO  cc. 

Time, 
Min. 

Rotation, 
degrees. 

Amt. 
inverted, 

«xio«. 

0 

13.17 

0 

15 

11.  '59 

9.38 

445 

30 

10.06 

18.46 

446 

60 

7.24 

35.19 

443 

90 

4.76 

49.91 

441 

120 

2.67 

62.31 

441 

180 

-0.26 

79.70 

441 

240 

-1.91 

89.50 

446 

300 

-2.72 

94.30 

443 

3days 

-3.71 

Mean 

,     443 

10.45 


Expts.  B36  and  B38. 
cc.  of  Invertase  6  per  100  cc. 


Av.  dev.,  0.40%. 

Expts.  B35  and  B37. 

10  cc.  of  boiled  Invertase  8  and  10.45  cc. 
of  Invertase  6  per  100  cc. 


Time, 
Min. 

Rotation, 
B36.                B38. 
Degrees. 

Amt. 
inverted, 
P,  %• 

wX10«. 

Time, 
Min. 

Rotation,                Amt. 
B35.                B37.    inverted,    nX10«. 
Degrees.                  p,  %. 

0 

13.14 

13 

,13 

0 

.  .  . 

0 

13.25 

13 

.24 



15 

11.55 

11 

.57 

9.38 

445 

15 

11.67 

11 

.67 

9.38 

445 

30 

10.04 

10 

,06 

18.34 

443 

30 

10.15 

10 

.16 

18.34 

443 

60 

7.27 

7, 

,29 

34.78 

437 

60 

7.36 

7 

.39 

34.84 

438 

90 

4.87 

4.88 

49.02 

432 

90 

4.94 

4 

.98 

49.20 

434 

120 

2.84 

2, 

.84 

61.13 

429 

120 

2.92 

2 

.94 

61.25 

430 

180 

-0.04 

-0 

06 

78.28 

426 

180 

-0.01 

0 

.04 

78.52 

428 

240 

-1.72 

-1 

.71 

88.13 

424 

240 

-1.67 

-1 

.64 

88.43 

429 

300 

-2.61 

-2 

59 

93.41 

422 

300 

-2.53 

-2 

.50 

93.53 

425 

3-6  days, 

,-3.72 

-3 

.72 
Av. 

Mean 
,  dev.,  1 

,  433 

.67%. 

2-5  das. 

-3.60 

o 

.61 
Av. 

Mean 
dev.  1. 

,  434 
38%. 

In  order  to  show  that  preparation  No.  3  had  not  become  normal  simply 
on  standing,  but  that  the  normal  course  of  the  reaction  was  really  pro- 
duced by  the  presence  of  the  boiled  invertase,  other  experiments  were 
run  with  Invertase  3  alone,  and  were  found  to  give  decreasing  values  of 
n,  as  before.  These  values,  however,  were  somewhat  smaller  than  those 
obtained  in  Expts.  B12  to  B15,  indicating  that  this  preparation  had 
appreciably  lost  activity  on  being  kept  in  the  ice-box  for  less  than  5  months. 

Further  experiments  were  made  with  the  abnormal  invertase  prepa- 
rations Nos.  3  and  6  in  the  presence  of  different  concentrations  of  sodium 
chloride.  The  results  are  given  in  Table  XI. 

The  figures  in  Table  XI  indicate  that  increasing  concentrations  of 
sodium  chloride  exert  an  increasing  retarding  effect  on  the  action  of  the 


24 


TABLE  XI. 
EFFECT  OF  SODIUM  CHLORIDE  ON  ABNORMAL  INVERTASE. 


Expt.   B44.                                                       Expt.   B43. 
1  .905  cc.  of  Invertase  3  per  100  cc.  in  0  .02  M  NaCl.     1  .905  cc.  of  Invertase  3  per  100  cc. 

in  0.05  M  NaCl. 

Time, 
/. 
Min. 

0 
17 

Rotation, 
degrees. 

13.05 
11.34 

Amt. 
inverted,          wXlO8. 
P,  %• 

Time, 

/. 
Min. 

0 
15 

Rotation, 
degrees. 

13.05 
11.54 

Amt. 
inverted,           «X10*. 

P,  %• 

0 
8.96            424 

10.15 

425 

30 

10.08 

17.63 

425 

30 

10.12 

17.39 

419 

60 

7.38 

33.65 

422 

60 

7.44 

33.29 

417 

90 

4.99 

47.83 

420 

90 

5.08 

47.30 

414 

120 

2.99 

59.70 

416 

120 

3.03 

59.47 

414 

180 

0.00 

77.45 

417 

180 

0.05 

77.15 

414 

240 

-1.73 

87.72 

419 

240 

-1.69 

1   87.48 

415 

300 

-2.64 

93.14 

416 

300 

-2.61 

92.94 

412 

2-3  days 

-3.80 

Mean, 

420 

2-4  days 

-3.82 

Mean 

,  416 

Av.  dev.,  0  . 

71%. 

Av.  dev.,  0. 

70%. 

Expt.   B42. 
1 .905  cc.  of  Invertase  3  per  100  cc.  in  0 . 1  M  NaCl. 


Expt.   B48. 

10 .45  cc.  of  Invertase  6  per  100  cc. 
in  0.1  MNaCl. 


Time, 
t. 
Min. 

Rotation, 
degrees. 

Amt. 
inverted, 
P,%. 

HXIO'. 

Time, 
t. 
Min. 

Rotation,   . 
degrees. 

Amt. 
inverted 
P,  %. 

WX10S. 

0 

13.05 

'o 

.  .  . 

0 

13.13 

0 

15 

11.58 

8.72 

413 

15 

11.61 

9.02 

427 

30 

10.16 

17.15 

413 

30 

10.17 

17.57 

423 

60 

7.50 

32.94 

410 

60 

7.52 

33.29 

417 

90 

5.14 

46.94 

410 

90 

5.19 

47.12 

412 

120 

3.13 

58.87 

408    - 

123 

3.02 

60.00 

408 

180 

0.14 

76.62 

408 

165 

0.86 

72.82 

407 

240 

-1.66 

87.30 

413 

225 

-1.17 

84.87 

408 

300 

-2.59 

92.82 

410 

300 

-2.47 

92.58 

405 

3  days 

-3.84 

Mean, 

411 

3-6  days 

-3.75 

Mean 

,     414 

Av.  dev.,  0.46%. 


Av.  dev.,  1.67%. 


invertase.  This  was  not  observed  in  the  work  of  Fales  and  Nelson18  at 
the  optimum  hydrogen-ion  concentration,  but  this  may  be  due  to  the  fact 
that  they  worked  with  a  very  much  smaller  sugar  concentration,  0.5  g. 
per  100  cc.  This  retardation,  however,  seems  to  have  more  effect  at  the 
beginning  of  the  hydrolysis  than  at  the  end  in  the  case  of  Invertase  3,  for 
in  Expt.  B42,  with  0.1  M  sodium  chloride,  the  values  of  n  were  constant 
and  the  action  must  be  classed  as  that  of  normal  invertase.  Invertase  6, 
however,  was  not  made  normal  by  0.1  M  sodium  chloride,  for  in  Expt. 
B48  the  values  of  n  decreased  as  much  as  ever.  An  experiment  with 
0.5  M  sodium  chloride  and  Invertase  6  gave  values  which  decreased  some- 
what less,  but  still  were  not  constant  enough  for  the  action  to  be  regarded 

18  Fales  and  Nelson,  J.  Am.  Chem.  Soc.,  37,  2769  (1915). 


25 


as  normal.     Unfortunately  the  supply  of  Invertase  6  became  too  low  for 
further  experiments  to  be  carried  out  with  it. 

Further  experiments  were  made  with  Invertase  3  to  determine  the  effect 
of  invertase  concentration  on  the  abnormal  action.  The  results  are  given 
in  Table  XII. 

TABLE  XII. 
ABNORMAL  INVERTASE  AT  DIFFERENT  CONCENTRATIONS. 


Expts.  B58  and  B59. 
0  .5  cc.  of  Invertase  3  per  100  cc. 

Expts.  B54  and  B55. 
3  cc.  of  Invertase  3  per  100  cc. 

Time, 
/. 
Min. 

Rotation,                Amt. 
B58.               B59.     inverted,       nXlQ6. 
Degrees.                p,  %. 

Time, 
Min. 

Rotation, 
B54.                   B55. 
Degrees. 

Amt. 
inverted, 
P,  %. 

«xio«. 

0 

13 

.05 

13.05 

0 

.  .  . 

0  ' 

13.06 

13.06 

0 

60 

11 

.53 

11.51 

9 

.08 

108 

10 

11.46 

11.48 

9.44 

671 

120 

10 

.06 

10.05 

17 

.80 

107 

20 

9.96 

9.98 

18.34 

664 

195 

8 

.35 

8.33 

27 

.95 

106 

30 

8.52 

8.55 

26.88 

662 

270 

6 

.72 

6.77 

37 

.45 

106 

45 

6.50 

6.53 

38.87 

660 

360 

5 

.06 

5.06 

47 

.42 

104 

70 

3.62 

3.67 

55.91 

654 

450 

3 

.50 

3.54 

56 

.56 

103 

100 

0.98 

71.69 

654 

540 

2 

.22 

2.20 

64 

.33 

102 

120 

-0.29 

-0.28 

79.23 

654 

1101 

-1. 

96 

.... 

89 

.08 

96 

150 

-1.62 

-1.62 

87.12 

656 

7  to  12 

Mean, 

104 

3  to  8 

Mean, 

659 

days 

-3 

.79 

-3.79 

Av. 

dev., 

2.7% 

days 

-3.79 

-3.79 

Av.  dev.,  0 

.74%. 

Time, 

ft 

B56. 

Min. 

0 

13.12 

6 

11.21 

12 

9.40 

18 

7.72 

26 

5.66 

35 

3.62 

48 

1.25 

65 

-0.88 

85 

-2.26 

4  to  5  days 

-3.75 

Expts.  B56  and  B57. 
6  cc.  of  Invertase  3  per  100  cc. 

Rotation, 


Degrees. 


B57. 


Amt. 
inverted, 


MX10«. 


13.12  0 

11.23  11.28  134 

9.43  22.02  134 

7.72  32.05  133 

5.66  44.27  133 

3.62  56.38  132 

1.30  70.33  132 

-0.84  82.97  134 

91 .28  135 

-3.74  Mean,  133 

Av.  dev.,  0.67%. 

These  results  show  that  in  the  case  of  Invertase  3  the  abnormality  decreases 
with  increasing  amount  of  invertase  or  increases  with  decreasing  amount 
of  invertase  or  increasing  time  of  reaction. 

It  is  not  possible  to  explain  these  changes  in  the  abnormality  of  Inver- 
tase 3  at  the  present  time. 

IX.    Attempts  to  Make  Normal  Invertase  Become  Abnormal. 

Since  the  presence  of  sodium  chloride  had  seemed  to  some  extent  to 
favor  the  normal  course  of  invertase  action,  it  seemed  worth  while  to  find 
out  whether  further  dialysis,  by  removing  any  last  traces  of  salt,  could 


26 

make  a  specimen  of  normal  invertase  act  abnormally.  Accordingly  a 
sample  of  Invertase  8  was  dialyzed  for  a  week  in  a  collodion  bag  against 
8  changes  of  distilled  water.  This  was  designated  as  Invertase  8A,  and 
when  tested  was  found  to  be  still  normal,  as  is  shown  by  the  results  in 
Table  XIII,  Expt.  B46. 

Another  sample  of  Invertase  8  was  partially  inactivated  by  heating  for 
1  hour  on  a  water-bath  at  50°,  and  then  for  l/z  hour  more  at  about  57°. 
This  reduced  its  activity  by  about  one-half.  This  invertase,  No.  8E, 
was  also  found  to  be  still  normal,  as  is  shown  by  Expts.  B50  and  B51, 
Table  XII. 

'  A  further  attempt  to  render  Invertase  8  abnormal  was  made  by  ex- 
posing some  of  it  for  2  hours,  in  a  quartz  flask,  to  the  ultraviolet  and  other 
radiation  given  by  a  mercury  arc  lamp.  The  result,  Invertase  8F,  had 
about  one-half  the  activity  of  Invertase  8,  but  was  also  found  to  be  still 
normal,  as  is  shown  by  Expts.  B52  and  B53,  Table  XIII. 

TABUS  XIII. 

ACTION  OF  NORMAL  INVERTASE  AFTER  FURTHER  DIALYSIS,  HEATING,  AND  EXPOSURE 

TO  THE  MERCURY  ARC. 


Expt.  B46. 
Invertase  8A,  dialysed,  5  cc.  per  100  cc. 

Time,                              Amt. 
t.             Rotation,  inverted,       nX10e. 
Min.         Degrees.      p,  %. 

0             13.06                  0 

Expts.  B50  and  B51. 
Invertase  8E,  heated,  5  cc.  per  100  cc. 

Time,                 Rotation,                    Amt. 
/.                B50.               B51.          inverted         nX10«. 
Min.                    Degrees.                    p,  %. 

0             13.10             13.10                  0 

15 

11.27 

10.62        505 

15           10.94           10.94         12.82 

612 

30 

9.56 

20.77        504 

30            8.88            8.89        25.04 

614 

60 

6.44 

39.29        501 

50            6.37            6.38        39.94 

612 

90 

3.78 

55.07        499 

70            4.18            4.19        52.94 

610 

120 

1.66 

67.66        497 

90            2.30            2.35        63.98 

610 

180 

-1.14 

84.27        501 

110            0.79            0.84        72.94 

612 

230 

-2.34 

91.39        502 

140         -0.87         -0.85        82.85 

618 

270 

-2.87 

94.54        499 

180         -2.20         -2.18        90.74 

624 

3  days 

-3.79 

Mean,    501 

2-5  days    -3.78         -3.78            Mean,    614 

Av.  dev.,  0.40%. 

Av.  dev., 

0.57%. 

Expts. 

B52  and  B53. 

Invertase  8F,  exposed  to  mercury  arc,  5  cc.  per  100  cc. 

Time, 

Rotation, 

Amt. 

/. 

B52. 

B53.                    inverted,                  nXlO*. 

Min. 

Degrees. 

P,  %• 

0 

13.09 

13.09                     0 

15 

10.33 

10.35                16.32                785 

25 

8.61 

8.63                26.53                783 

35 

6.99 

7.04                36.08               781 

45 

5.51 

5.53                44.92                779 

65 

2.93 

2.99                60.12                775 

85 

0.94 

0.97              "72.05                776 

105 

-0.54 

-0.53                80.89                781 

140 

-2.12 

-2.12                90.27                787 

1  to  3  days 

—3.77 

—3  80                             Mean,  781 

Av.  dev.,  0.38%. 

27 

Since  the  values  of  n  in  Table  XIII  are  constant  in  each  experiment, 
having  an  average  deviation  from  the  mean  in  each  case  of  less  than  0.7%, 
the  results  show  that  the  invertase  was  still  acting  normally.  Hence  it 
may  be  concluded  that  it  is  not  possible  by  any  of  these  three  methods 
of  treatment  to  render  a  normal  invertase  preparation  abnormal. 

X.     Experimental  Details. 

Preparation  of  materials. — The  invertase  used  was  all  obtained  from 
yeast  by  the  method  of  Nelson  and  Born,19  with  slight  modifications  as 
described  below.  Preparations  6  and  7  had  been  made  by  previous  workers 
in  this  laboratory  and  had  been  kept  for  several  years  in  solution,  saturated 
with  toluene,  in  an  ice-box.  Preparations  1,  2  and  3  were  made  from 
yeast  which  had  been  permitted  to  autolyze  for  about  a  month  and  then 
filtered,  and  the  filtrate  had  been  treated  with  toluene  and  kept  in  stoppered 
bottles  at  room  temperature  for  three  years  or  more.  During  this  time 
more  solid  matter  had  separated,  and  this  was  filtered  off  and  the  filtrate 
treated  according  to  the  method  described  by  Nelson  and  Born19  with  the 
following  modifications.  Only  one  precipitation  with  alcohol  was  used 
and  the  kaolin  treatment  was  omitted.  After  treatment  with  lead  acetate 
and  potassium  oxalate,  the  filtrate  was  dialyzed  for  from  4  to  6  days  in 
collodion  bags  against  running  tap  water.  The  solutions  become  colorless 
and  nearly  clear  during  the  dialysis.  The  dialyzed  solutions  were  not 
precipitated  again,  but  were  preserved  with  toluene  and  kept  in  the  ice-box 
until  needed  for  the  experiments.  Preparation  No.  8  was  prepared  by 
the  same  method  from  a  new  lot  of  100  pounds  of  pressed  yeast.2Q  The 
preparation  of  Invertase  No.  2  was  carried  out  by  Nelson  and  Simons,21 
who  modified  the  treatment  further  by  nearly  neutralizing  the  solution 
with  ammonia  before  the  alcohol  precipitation.  No  differences  in  the 
method  of  preparation  are  known  which  might  account  for  the  abnor- 
mality of  invertase  preparations  Nos.  3  and  6. 

Two  lots  of  sucrose  were  used.  In  each  case  the  starting  point  was  the  best  com- 
mercial sugar,  which  was  dissolved  in  distilled  water  and  clarified  with  charcoal.  The 
first  lot  was  precipitated  by  alcohol  by  the  method  of  Cohen  and  Commelin.22  Its 
rotation  was  found  to  agree  within  0.1%  with  that  calculated  from  the  formulas  of 
Landolt  and  Schonrock.23  The  second  lot  was  recrystallized  from  water  by  a  procedure 
similar  to  that  of  Bates  and  Jackson.24  Its  rotation  agreed  with  the  calculated  value 
within  0.04%. 

Other  chemicals  were  c.  p.  grades,  used  without  further  purification. 

19  Nelson  and  Born,  J.  Am.  Chem.  Soc.,  36,  393  (1914). 

20  Kindly  furnished  by  the  Jacob  Ruppert  Brewery  of  New  York  City. 

21  Simons,  Dissertation,  Columbia  University,  1921;  Nelson  and  Simons,    J.  Am. 
Chem.  Soc.,  (to  be  published  later). 

22  Cohen  and  Commelin,  Z.  physik.  Chem.,  64,  29  (1908). 

23  Browne,  "A  Handbook  of  Sugar  Analysis,"  John  Wiley  and  Sons,  New  York, 
1912,  pp.  177-8. 

24  Bates  and  Jackson,  Bur.  of  Standards  Sci.  Papers,  No.  268,   75  (1916). 


28 

Apparatus. — Constant  temperature  was  obtained  by  the  use  of  an 
electrically  controlled  water-bath  which  remained  at  25°  ±0.01°. 

The  progress  of  the  inversion  was  followed  by  means  of  a  Schmidt  and 
Haensch  polarimeter  reading  to  0.01°.  The  tubes  used  were  200  mm. 
long,  and  were  proved  to  be  of  the  same  length  by  observing  the  rotation 
of  the  same  10%  sugar  solution  in  each  tube.  The  temperature  of  the 
tubes  was  kept  constant  by  the.  thermostat  described  by  Nelson  and 
Beegle,25  which  maintained  a  temperature  of  25°  ±0.05°. 

Monochromatic  light  of  wave  length  546.1  /*//  was  obtained  from  a 
mercury  vapor  arc  by  purification  through  two  Wratten  filters,  one  a 
No.  77,  and  the  other  a  No.  77  which  had  been  re-cemented  with  a  green 
film  in  place  of  the  yellow  one.  Thanks  are  due  to  Dr.  C.  B.  K.  Mees  of 
the  Eastman  Kodak  Company  for  preparing  these  filters.  This  light 
made  it  possible  to  use  the  polariscope  with  a  half -shadow  angle  of  0.5°. 

Nonsol  bottles  were  used  to  contain  the  solutions  undergoing  hydrolysis. 
All  volumetric  apparatus  used  in  making  up  solutions  was  calibrated. 

Control  of  the  Hydrogen-ion  Concentration. — The  desired  hydrogen-ion 
concentration  was  obtained  by  the  use  of  a  buffer  mixture  of  0.1  M  acetic 
acid  and  0.1  M  sodium  acetate  in  the  proportions  given  by  Michaelis.26 
One  hundred  cc.  of  the  final  solution  always  contained  10  cc.  of  this  buffer, 
making  the  total  concentration  0.01  M.  This  concentration  was  low 
enough  so  that  any  salt  effect  on  the  invertase  action  was  negligible,  espec- 
ially at  the  optimum  hydrogen-ion  concentration.18  In  the  experiments 
of  Nelson  and  Vosburgh1  the  desired  hydrogen-ion  concentration  was 
obtained  by  the  use  of  diluted  hydrochloric  acid.  In  the  experiments  of 
Vosburgh  and  Nelson14  a  buffer  of  citric  acid  and  secondary  sodium  citrate 
was  used  at  a  total  citrate  concentration  of  0.01  M. 

The  hydrogen-ion  concentration  was  measured  during  or  after  each 
inversion  by  the  colorimetric  method  of  Sorensen,15  using  a-naphthyl- 
amino-azo-^-benzene  sulfonic  acid  as  indicator  with  citrate  standards. 
The  latter  were  standardized  electrometrically  with  the  hydrogen  electrode 
and  the  saturated  potassium  chloride  calomel  cell27  using  a  salt  bridge  of 
saturated  potassium  chloride  solution.  The  hydrogen-ion  concentrations 
were  based  on  0.1000  M  hydrochloric  acid  as  a  standard,  its  ionization28 
being  taken  as  92.04%  at  25,  °  the  temperature  at  which  the  present  deter- 
minations were  made. 

Procedure. — In  general  the  procedure  followed  was  that  recommended 
by  Vosburgh.16  Duplicate  experiments  were  run  on  different  days  with 
freshly  prepared  sugar  solutions.  A  solution  was  made  up  containing 

25  Nelson  and  Beegle,  /.  Am.  Chem.  Soc.,  41,  559  (1919). 

26  Michaelis,  "Die  Wasserstoffionenkonzentration,"  Springer,  Berlin,  1914,  p.  184. 

27  Kales  and  Mudge,  /.  Am.  Chem.  Soc.,  42,  2434  (1920). 
28Fales  and  Vosburgh,  ibid.,  40,  1295  (1918). 


29 

sucrose  and  buffer  in  such  concentrations  that  when  a  certain  volume  of 
this  had  been  measured  out  it  would  be  possible  to  add  from  a  pipet  a 
round  number  of  cubic  centimeters  of  invertase  to  start  the  reaction.  For  ex- 
ample, in  Bxpt.  Bl  32.680  g.  of  sucrose  and  32.68  cc.  of  buffer  were  diluted  to 
500  cc.  at  25  °.  Of  this  solution  321.80  cc.  was  pipetted  into  a  Nonsol  bottle, 
and  5  cc.  of  invertase  was  added  to  start  the  reaction.  This  produced 
the  initial  concentrations  given  in  Table  I  A.  The  solutions  were  stirred 
by  a  current  of  filtered  air  while  being  mixed,  and.  samples  were  taken 
by  pipets  delivering  in  10  seconds  or  less.21  The  time  of  mixing  or  of 
sampling  was  taken  as  the  mean  time  of  delivery  of  the  pipet  used.  The 
reaction  was  stopped  and  mutarotation  hastened  by  the  use  of  sodium 
carbonate  as  recommended  by  Hudson,29  a  25cc.  sample  being  added  to 
5  cc.  of  0.1  M  sodium  carbonate  solution.  The  initial  rotation  of  each 
solution  was  determined  by  preparing  samples  of  identical  composition 
in  which  the  sodium  carbonate  was  added  to  the  sugar  before  the  addition 
of  the  invertase,  thus  rendering  the  invertase  entirely  inactive.  The 
rotation  of  each  solution  was  determined  by  taking  the  mean  of  at  least 
four  concordant  readings,  the  tube  being  rotated  slightly  after  each  reading 
to  ensure  the  detection  of  any  strain  in  the  cover  glasses.30  The  zero  point 
of  the  polariscope  was  similarly  determined  by  the  use  of  a  tube  filled  with 
distilled  water.  The  final  rotations  were  obtained  by  taking  samples  2 
days  or  more  after  the  start  of  the  reaction.  Samples  taken  on  the  second 
and  third  days  usually  had  the  same  rotation.  In  calculating  the  per- 
centage inverted,  the  total  change  in  rotation  was  always  taken  as  16.85°, 
since  this  value  was  obtained  in  all  the  experiments  of  Vosburgh  and 
Nelson14  as  well  as  in  the  majority  of  the  present  experiments. 

Since  in  several  experiments  the  total  change  in  rotation  appeared  to 
be  a  few  hundredths  of  a  degree  more  than  16.85°,  it  was  thought  ad- 
visable to  test  the  effect  of  such  differences  on  the  values  of  n  as  obtained 
by  the  use  of  Equation  12.  A  sample  calculation  was  made  for  Expt. 
B46,  Table  XIII,  with  the  following  results. 

Using  16.85°,  Using  16.89°, 

nX10«.  nXlO*. 

505  501  504  498 

504  502  503  497 

501  499  500  492 

499  Mean,  501  497  Mean,  498 

497  Av.dev.,0.40%  495  Av.  dev.,0.60%. 

These  results  show  that  an  error  of  0.04°  in  determining  the  total  change 
in  rotation  could  not  have  caused  sufficient  error  in  the  values  of  n  to  make 
a  normal  invertase  preparation  appear  abnormal.  Since  this  was  the 

29  Hudson,   /.  Am.  Chem.  Soc.,  30,   1564   (1908). 
80  Browne,  Ref.  23,  p.  156. 


30 

extreme  deviation  noticed  from  the  value  16.85°,  the  procedure  adopted 
of  taking  the  total  change  as  16.85°  in  all  calculations  is  quite  justified. 
A  calculation  of  the  possible  error  in  determining  the  rotation  of  any 
sample  which  might  be  due  to  errors  in  the  various  measurements  of  weight 
and  volume  involved  in  this  procedure  has  been  made  by  Messrs.  G.  Bloom- 
field  and  F.  Hollander  of  this  laboratory.  Using  estimates  of  these  errors 
based  on  the  present  authors'  calibrations,  this  calculation  gave  a  maxi- 
mum error  of  about  0.01°  in  the  determination  of  the  rotation  of  a  sample. 
Since  the  duplicate  experiments  did  not  always  agree  so  well  as  this,  a 
fairer  estimate  of  the  precision  of  the  measurements  may  be  obtained  from 
the  agreement  of  the  duplicates  themselves.  This  would  put  the  average 
difference  between  duplicate  measurements  of  a  change  in  rotation  at 
about  0.02°.  The  effect  of  such  an  error  on  the  values  of  n  obtained  by 
the  use  of  Equation  12  has  already  been  considered. 

Summary. 

1.  It  has  been  shown  that  not  all  preparations  of  yeast  invertase  are 
alike  in  their  action,  but  that  some  are  abnormal  in  allowing  the  hydrolysis 
of  cane  sugar  to  slow  up  more  than  others  after  the  first  20%  of  the  inver- 
sion. 

2.  An  empirical  equation  is  given  which  fits  the  hydrolysis  of  cane  sugar 
by  normal  invertase  over  an  extreme  range  of  invertase  concentration  of 
12  :1.     By  this  means  it  has  been  shown  that  the  hydrolysis-time  curves 
for  normal  invertase  are  of  the  same  shape  for  these  different  invertase 
concentrations  and  can  be  made  to  superimpose  if  the  time  scale  be  multi- 
plied by  the  proper  constant. 

3.  By  the  same  method  it  has  been  shown  that  the  hydrolysis  curve 
with  normal  invertase  has  the  same  shape  at  temperatures  varying  from 
15°  to  35°,  and  at  hydrogen-ion  concentrations  from 4.0  X  10~5  to  3.2  X 
10~7. 

4.  It  was  found  that  one  abnormal  invertase  preparation  could  be  ren- 
dered normal  by  the  presence  of  .boiled  normal  invertase  or  0.1  M  sodium 
chloride,  while  another  was  not  affected  by  either.    The  former  preparation 
also  worked  normally  at  a  very  high  concentration. 

5.  It  was  found  impossible  to  render  a  normal   invertase   preparation 
abnormal  by  further  dialysis  or  partial  inactivation  by  heating  or  ultra- 
violet light. 


VITA. 

David  Ingersoll  Hitchcock  was  born  in  Detroit,  Michigan,  on  June  26, 
1893.  In  1911  he  was  graduated  from  the  Detroit  Central  High  School. 
In  1915  he  was  graduated  from  Dartmouth  College  with  the  degree  of 
Bachelor  of  Arts.  From  1915  to  1917  he  was  Instructor  in  Chemistry  at 
Dartmouth  College.  He  was  a  graduate  student  in  Chemistry  at  Columbia 
University  during  the  summers  of  1915,  1916,  and  1917.  In  August,  1917, 
he  enlisted  in  the  101st  Machine  Gun  Battalion  of  the  26th  Division, 
United  States  Army.  In  June,  1918,  he  was  transferred  to  the  Gas  Service, 
later  the  Chemical  Warfare  Service,  and  was  assigned  to  the  chemical 
laboratory  "at  Hanlon  Field,  Chaumont,  France.  In  January,  1919,'  he  was 
discharged  from  the  Army.  Since  February,  1919,  he  has  continued  his 
studies  at  Columbia  University,  where  he  received  the  degree  of  Master 
of  Arts  in  1919.  He  has  been  laboratory  assistant  in  various  courses  in 
the  Department  of  Chemistry.  Since  February,  1920,  he  has  been  Harri- 
man  Research  Assistant  in  the  laboratory  of  Professor  J.  M.  Nelson.  He 
is  co-author  with  Professor  Nelson  of  a  paper  on  "The  Activity  of  Ad- 
sorbed Invertase,"  which  has  been  accepted  for  publication  in  the  Journal 
of  the  American  Chemical  Society.  For  the  year  1921-1922  he  has  been 
appointed  a  Fellow  of  the  Rockefeller  Institute  for  Medical  Research, 
New  York  City. 


THIS  BOOK  IS  DUE  ON  THE  LAST  DATE 
STAMPED  BELOW 


AN  INITIAL  FINE  OF  25  CENTS 

WILL  BE  ASSESSED   FOR   FAILURE  TO   RETURN 
THIS   BOOK  ON   THE   DATE  DUE.   THE  PENALTY 
WILL  INCREASE  TO  SO  CENTS  ON  THE  FOURTH 
DAY    AND    TO    $t.OO    ON     THE    SEVENTH     DAY 
OVERDUE. 

NOV     2    1939 

NQV  #    ,, 

V  . 

**•*,       J, 

?0,_ 

LD  21-100m-7,'39(402s) 

478726       /J( 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 


